1. Preparing for AMC 12 is NOT much harder than preparing for AMC 10
The additional topics tested on the AMC 12 but not on the AMC 10 are related to precalculus, including logarithms, complex numbers, trigonometry, conics, and advanced three-dimensional coordinate geometry. A student who plans to take AMC 10 has a lighter learning burden of not having to learn these materials. However, this is NOT a good strategy to prepare for AMC 10 due to the following reasons.
(1) These additional materials are very useful in solving AMC 10 problems although they are not directly tested on AMC 10.
For instance, in some AMC 10 geometry problems, it is necessary to add auxiliary lines for facilitating the analysis. But adding auxiliary lines is generally trick and complicated, and is a topic that requires lots of creative thinking to be learned. No student can guarantee that he/she can always find appropriate auxiliary lines to add on the AMC 10 contest in a very limited time. However, many such problems can be easily and quickly solved in a more straightforward manner by using trigonometry without adding any auxiliary line.
Hence, learning additional materials enables a student to own more powerful tools to easily solve some AMC 10 problems that are very challenging without these tools.
(2) These precalculus materials are not hard to learn.
A student can easily learn these materials. Many students find them no different from other branches of mathematics and pick up on them quickly.
Math analysis is the branch of Precalculus that many students find easier to grasp. It feels familiar due to the similarities to algebra.
2. It is easier to qualify for the AIME through AMC 12 Than through AMC 10
(1) The percent of AMC 10 contestants to qualify for the AIME is only half of the percent of AMC 12 contestants.
The curve for the AMC 12 is much more generous. In fact, for AMC 10, invitations for taking the AIME are issued to the top 2.5% of all scorers. For AMC 12, invitations for taking the AIME are issued to the top 5% of all scorers.
(2) The cutoff scores for AMC 10 contestants eligible to qualify for the AIME are approximately 14% to 24% higher than that for AMC 12 contestants.
It is easier to achieve the AMC 12 cutoff scores than the AMC 10 cutoff scores. The AMC 10 and the AMC 12 contests have about 10 to 15 questions in common. Two contests have 40% to 60% overlapping questions, and the difficulty levels of a majority of these questions are easy.
The following are cutoff scores for AIME qualification from 2019 to 2021.
|Year||AMC 10A||AMC 10B||AMC 12A||AMC 12B|
In fall 2022, the AMC 10A and AMC 12A had 12 overlapping questions, and the AMC 10B and AMC 12B had 11 overlapping questions, as shown in The 2021 Fall AMC 10 and AMC 12 Have 11 to 12 Questions in Common.
For instance, in 2022 Fall version B tests, the AIME floor for the AMC 10 was 96, 14.3% higher than the floor for AMC 12, 84. Even if the AMC 12 problems are more difficult, the difference in 12 points is just from two problems. To qualify for AIME through the AMC 10, the minimum correct answers needed are 15 to 16. For the AMC 12, however, you only need at least 13 correct answers.
Furthermore, the AMC 12 questions have about at least 9 questions out of the first 15 that are the same as the AMC 10’s and they do not get significantly harder until after Question 16. In fact, the difficulty level of most of these overlapping questions are easy or medium. This entails that beyond correctly answering most of their overlapping questions, a student taking the AMC 12 only needs to correctly answer very few nonoverlapping questions. By contrast, a student taking the AMC 10 needs to correctly answer much more than that.
Hence, it is easier to qualify for the AIME through the AMC 12 than the AMC 10. Even for a student in grades 10 and below, who is familiar with trigonometry and precalculus, it easier to achieve the AIME floor score on the AMC 12 than on the AMC 10.
See more at:
- It Is Easier to Qualify for the AIME Through the AMC 12 Than Through the AMC 10
- The 2021 Fall AMC 10 and AMC 12 Have 11 to 12 Questions in Common
- This Year It Was Much Easier to Qualify for the AIME Through the AMC 12A ThanThrough the AMC 10A
- AMC 10 versus AMC 12
- Every Student Should Take Both the AMC 10A/12A and 10 B/12B!
- The AMC 10 and AMC 12 Have 10-15 Questions in Common
- Students Can Easily Qualify for the AIME Through the AMC 12 During 11th and 12th Grades
- How the AMC contests can help you get into the Ivy League Schools
More details can be found at:
- 365-hour Project to Qualify for the AIME through the AMC 10/12 Contests
- American Mathematics Contest 10 (AMC 10)
- American Mathematics Contest 12 — AMC 12
- Notable Achievements of Our Students
- AMC 10/12 Historical Results
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